Trying to read a string of binary 1's and 0's can seem a daunting task. However, with a bit of logic we can figure out what they mean. Humans have adapted to use a base ten number system simply because we have ten fingers. Computers, on the other hand (no pun intended), have only two "fingers"--on and off or one and zero. Therefore, the base two number system has been created.[1]

Steps

Method1

With Exponents

1

Find a binary number you want to convert. We'll use this as an example: 101010.

2

Multiply each binary digit by two to the power of its place number.[2] Remember, binary is read from right to left.[3] The rightmost place number being zero.

3

Add all the results together. Let's go from right to left.

0 × 20 = 0

1 × 21 = 2

0 × 22 = 0

1 × 23 = 8

0 × 24 = 0

1 × 25 = 32

Total = 42

Method2

Alternative Format with Exponents

1

Pick a binary number. Let's use 101. Here is the same method but in a slightly different format. You may find this format easier to understand.

101= (1X2) power of 2 + (0X2) power of 1 + (1X2) power 0

101= (2X2) + (0X0) + (1)

101= 4 + 0 + 1

101= 5

The 'zero' is not a number, but its place value must be noted.

Method3

Slot Value

1

Find your number. The example we'll use is 00101010.

2

Read from right to left. With each slot, the values are doubled. The first digit from the right has a value of 1, the second is a 2, then a 4, and so on.[4]

3

Add the values of the ones. The zeros are assigned their correlating number, but those numbers are not added.

So, in this example, add 2, 8, and 32. The result is 42.

There is a 'no' on 1, a 'yes' on 2, a 'no' on 4, a 'yes' on 8, a 'no' on 16, a 'yes' on 32, a 'no' on 64 and a 'no' on 128. "Yes" means to add, "no" is to skip. You can stop at the last one-digit.

It really depends on the method you're using. If you're looking for a sentence conversion, then the computer automatically reads in sets of eight e.g 00111111 (?), 00111101 (=), 01000001 (A) etc. However, the process the computer goes through is much more complicated than that. Essentially, every five digits is equal to either a symbol, number, or letter.

You can encode letters as binary using an encoding scheme (Unicode, etc.) and send the binary to someone else. The other person has to decode the binary back into letters using that encoding. Bytes (8 bits) can be thought of as numbers between 0-256, and most characters can be encoded as single bytes.

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Tips

Binary counts just like normal numbers. The rightmost digit increments by one until it cannot increase any more (in this case from 0 to 1) and then increments the next digit to the left by one and starts again at zero.

The numbers we deal with today have a place value. Assuming we are working with whole numbers, the right-most digit is the one's place, the next right-most digit is the ten's place, then hundred's, and so on. The place value for binary numbers go from one's, two's, four's, eight's, and so on.[5]

To read binary, find a number that you want to read, and remember to count the places from right to left. Then, multiply each digit by 2 to the power of its place number. For example, if the 3rd place from the right is a 1, you would multiply 1 by 2 to the power of 3 to get 8. Once you have an answer for each place, add the numbers together from right to left. For example, 101 would translate to the number 9. For tips on using other techniques, like exponents or slot value, read on!

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